The events of the ongoing credit crisis and past financial crises have emphasized the necessity for appropriate risk measures. The use of quantitative risk measures has become an essential management tool providing advice, analysis and support for financial and asset management decisions to market participants and regulators.
The most widely used risk measure is Value at Risk (VaR). VaR measures the maximum loss which a financial operator can incur over a defined time horizon and for a given confidence level. Its clear meaning and computational ease made it very popular among practitioners, so much so that it has largely contaminated the banking regulatory framework. However, VaR has a number of drawbacks ([1]}, [2]}). First, VaR blackdoes not
account for tail risk, i.e. it does not warn us about the size of the losses that occur with a probability lower than the predetermined confidence level. Second, VaR is not a “coherent" risk measure ([2]}) since it blackdoes not satisfy the sub-additivity property, and hence, it does not take into consideration the benefits of diversification. As a result, investors and risk managers are likely to construct positions with unintended weaknesses that result in greater losses under conditions beyond the VaR level ([4]}). Market participants could solve such problems by adopting the Expected Shortfall (ES) risk measure, which is defined as the conditional expectation of exceedances beyond VaR (see [5]} and [6]}). Unlike VaR, ES is a coherent risk measure and provides more information on the shape and the heaviness of the tails of the loss distribution. Therefore, ES has gained increasing attention from risk managers, banking regulators and investors as an alternative measure of risk, complementing the VaR measure.
